Hi Carpenter AND tile guy here :)In my opinion, if there is ANY shifting in a counter due to pressure, it's a bad install. however, to be safe, this could be mitigated by something like construction adhesive a strong patch across the bottom of the joint and then grout the whole thing full.

Additionally, saying 'caulk /silicone grout' for that area is kind of not the full picture:A premix siliconized grout is going to largely be trash that you should not use. Same with most silicone caulks. Most will begin to grow mold within a few years. I'd sooner not seal the backsplash at all but seal the countertop to the wall to achieve watertightness. Then just let the backsplash sit on top glued to the wall. This also solves the problem of walls that are not at all even with their friendly countertops to where they really only line up at the corners. No point putting any kind of grout like that as it will absolutely break .

Sorry for the tldr

My opinion for OP:Squirt "PHENOSEAL" into the crack from the bottom, but leave the upper ~1/8" for filling with a grout that you actually mix up yourself, and make sure it is UNSANDED

my first tile job I used it on slate without knowing that it was harder to clean than normal grout. Took twice as long to clean as the entire rest of the job took.